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@arXiv_mathAC_bot@mastoxiv.page
2024-06-18 09:25:50

This https://arxiv.org/abs/2312.12555 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Ring of invariants of an exponential map of a polynomial ring
Let $k$ be a field of arbitrary characteristic. We prove the following: $\bullet$ Let $B=k^{[3]}$ and $δ\in \mathrm{EXP}(B)$ be non-trivial. If the plinth ideal $(\mathrm{pl} (δ))$ contains a quasi-basic element, then the ring of invariants ($B^δ$) is $k^{[2]}$. $\bullet$ Let $B=R^{[n]}$, where $R$ is a $k$-domain and $δ\in \mathrm{EXP}_R(B)$ is a triangular exponential map. Then $B^δ$ is non-rigid. We prove the following results for a $k$-domain $R$ when the characteristic of $k$ is…